Dear All,
While using the -nl- command I have come across a
rather puzzling result. Two different specifications
that fit the data equally well (the correlation from
their predicted values is 1) show an r-squared of
0.1 and 0.7 respectively.
It seems that in one of the models stata is
incorrectly calculating the sum of squares from the
model (I could replicate the value for one of the
models but not for the other).
Any hint to what is happening? It seems to me like a
bug but I may be overlooking something. I also dont
understand why the degrees of freedom is 3 in one
model and 4 in the other.
Here is the code and results:
**************************************************
. program define nlpark1
1. version 7
2. if "`1'"=="?" {
3. global S_1 "b2 b3 b4 b5"
4. global b2=0
5. global b3=.01
6. global b4=0
7. global b5=10
8. exit
9. }
10. replace `1'
=exp($b2)*exp($b3*time)+exp($b4)*exp(-$b5*time)
11. end
.
. program define nlpark2
1. version 7
2. if "`1'"=="?" {
3. global S_1 "b2 b3 b4 b5"
4. global b2=0
5. global b3=.01
6. global b4=0
7. global b5=10
8. exit
9. }
10. replace `1'
=$b2+$b3*time+exp($b4)*exp(-$b5*time)
11. end
.
.
. use final
. drop if total==.|total==0
(10 observations deleted)
. gen time=days0/365.25
. drop if time==.
(0 observations deleted)
. sum total if days0==0
Variable | Obs Mean Std. Dev.
Min Max
-------------+-----------------------------------------------------
total | 150 31.09333 12.82777
6.5 73
. local avdep=r(mean)
. local startv=log(`avdep'/2)
. nl park1 total, eps(1e-9) init(b2=
`startv',b4=`startv')
(obs = 1576)
Iteration 0: residual SS = 204943.1
...
Iteration 6: residual SS = 196084.1
Source | SS df MS
Number of obs = 1576
-------------+------------------------------
F( 4, 1572) = 1342.48
Model | 669821.354 4 167455.339
Prob > F = 0.0000
Residual | 196084.146 1572 124.735462
R-squared = 0.7736
-------------+------------------------------
Adj R-squared = 0.7730
Total | 865905.5 1576 549.432424
Root MSE = 11.1685
Res. dev. = 12074.57
(park1)
------------------------------------------------------------------------------
total | Coef. Std. Err. t P>|t|
[95% Conf. Interval]
-------------+----------------------------------------------------------------
b2 | 2.805342 .0511239 54.87 0.000
2.705063 2.90562
b3 | .0977053 .0379304 2.58 0.010
.0233058 .1721048
b4 | 2.673872 .0815743 32.78 0.000
2.513866 2.833877
b5 | 10.69553 2.007598 5.33 0.000
6.757673 14.63338
------------------------------------------------------------------------------
(SE's, P values, CI's, and correlations are
asymptotic approximations)
. predict tm1
(option yhat assumed; fitted values)
. nl park2 total, eps(1e-9) init(b2=
`startv',b4=`startv')
(obs = 1576)
Iteration 0: residual SS = 547186.4
...
Iteration 5: residual SS = 196080.5
Source | SS df MS
Number of obs = 1576
-------------+------------------------------
F( 3, 1572) = 60.60
Model | 22675.1691 3 7558.38969
Prob > F = 0.0000
Residual | 196080.524 1572 124.733158
R-squared = 0.1037
-------------+------------------------------
Adj R-squared = 0.1019
Total | 218755.693 1575 138.892503
Root MSE = 11.1684
Res. dev. = 12074.54
(park2)
------------------------------------------------------------------------------
total | Coef. Std. Err. t P>|t|
[95% Conf. Interval]
-------------+----------------------------------------------------------------
b2 | 16.42274 .9216482 17.82 0.000
14.61495 18.23053
b3 | 1.824629 .7069261 2.58 0.010
.438012 3.211246
b4 | 2.681091 .0842907 31.81 0.000
2.515757 2.846425
b5 | 10.5638 2.023805 5.22 0.000
6.594161 14.53344
------------------------------------------------------------------------------
* Parameter b2 taken as constant term in model & ANOVA
table
(SE's, P values, CI's, and correlations are
asymptotic approximations)
. predict tm2
(option yhat assumed; fitted values)
. corr tm1 tm2
(obs=1576)
| tm1 tm2
-------------+------------------
tm1 | 1.0000
tm2 | 1.0000 1.0000
**************************************************
thanks
Paulo Guimaraes
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